2 Assumptions 1. 'Typical' spa is assumed to have the following conservative measures: a) Area = 6 m 2, b) Average Water temperature = 38 C c) Jets = 4 d) Pumps = 1 e) Jet Pump Timer = 15 min. max. f) Plumbing = 2 in. g) Tap Water temperature = 20 C 2. Spa Location = California - Indoor (outdoor spas experience significantly greater evaporation due to wind). 3. The average temperature of tap water equals the average temperature of the climate. 4. Standard atmospheric pressure = Pa 5. Average Air humidity = 60% 6. Average Air Temperature = 25 C 7. Ambient airflow over water of unjetted spa is the same as unoccupied jetted spa. 8. Unjetted spa water surface is undisturbed (i.e., indoor with no wind). 9. Jets run for a total average of 30 min/day while spa is unoccupied (i.e., as few as 3 people leaving the spa unoccupied with 10 min. remaining on the timer). 10. The spa is open to the public an average of 30 days month No blower is used to create bubbles. I. Introduction Spas are major energy consumers, and, by virtue, they represent a significant opportunity for energy conservation. The vast majority of energy consumed by spas is to counteract the effects of evaporation. Evaporation occurs when liquid molecules near the surface experience collisions that increase their energy above that needed to overcome the surface binding energy. When those higher energy molecules break away from the water into vapor, the remaining water molecules move slightly slower. Thus when water evaporates, the spa drops in temperature. As a result, the spa needs to be reheated to the intended temperature. Evaporation from indoor spas impose a greater concern by increasing the load on HVAC systems, shortening HVAC and spa equipment life-cycles, as well as the usable life of building materials. The evaporation also increases the risk of exposing users to chemical and microbial hazards. 1 1 See generally, World Health Organization (2006) Guidelines for safe recreational water environments. Volume 2, Swimming pools and similar environments. Last accessed May 1,

3 There is no known prior study of the effects of spa jets on evaporation. II. Baseline Evaporation The baseline evaporation is the amount of water evaporating when the spa jets are off. Many empirical studies since the late 19 th century model evaporation from pools. Recently, computer Computational Fluid Dynamics software has been coupled with these empirical studies to determine the best formula for swimming pool evaporation. 2 One such study compared the most commonly cited evaporation formulas and concluded M.M. Shah's model for evaporation from pools and spas to be most reliable. 3 Shah's formula has also been validated by the American Society of Heating, Refrigerating and Air-conditioning Engineers (ASHRAE). 4 While Shah has further developed his well known formula for evaporation from unoccupied pools to more precisely account for ambient air flow, because we assume ambient airflow to be constant between our unjetted and jetted spa comparisons, we will use Shah's simpler non-airflow formula: 5 E = 35ρ r (ρ r ρ w ) 1/3 (W w W r ) (1) The specific density of moist air (ρ), the mass of moist air per volume of moist air, is the inverse of specific volume (v) of moist air, the volume of moist air per mass of moist air: 6 ρ = (1/v) (2) The specific volume (v) of moist air is: 7 v = RT / (p atm p w ) (3) The pressure of water vapor (p w ) relates to the assumed relative humidity (ф) as: 8 2 See generally, Li, Z., Heiselberg, P. (2005): CFC Simulations for Water Evaporation and Airflow Movement in Swimming Baths. Instituttet for Bygningsteknik: Aalborg Universitet. Last accessed May 1, Id. at p See generally, Shah, M.M., (2012): Calculation of Evaporation from Indoor Swimming Pools: Further Development of Formulas, ASHRAE Transactions 2012, Volume 118, Part 2. %20Evap%202012%20ASHRAE%20Trans.pdf. Last accessed May 1, Id. Equation (3). 6 National Aeronautics and Space Association. Last accessed May 1, ASHRAE Fundamentals Handbook 2001, Chapter 6, Equation (11). %20HVAC%202001%20Fundamentals%20Handbook.pdf. Last accessed May 1, Id. Equation (13). 3

5 v w = ( ) / ( ) Using Equation (2), the respective specific volumes can be converted to specific densities: ρ r = ρ w = Using these specific densities and humidity ratios in Equation (1), the typical spa's evaporation under the assumed conditions, while jets are off, is: E = 35( )( ) 1/3 ( ) E = kg h -1 m -2 III. Evaporation Caused by Running Jets Aeration is the bubbling of water (like jetting a spa). Aeration promotes evaporation in two ways: within the bubbles and at the surface where the bubbles burst. The greater the airflow rate, the greater the increase in evaporation due to aeration. 11 Spas typically create jetted bubbles by using the venturi effect. Here, we conservatively assume the more energy efficient venturi effect is the only method used to create bubbles. Venturi tubes use converging and diverging tube angles to change water pressure and velocity (as shown in Figure 2). Venturi jets have an air inlet which pulls air into the jet mixing the air and water to produce jetted bubbles (as shown in Figure 1). When the water inlet angles reduce the water pressure below atmospheric pressure, a pressure vacuum pulls air into the tube. The air and water join in the diverging portion of the tube where velocity is converted back to higher pressure air/water mixture which emerges into the spa as bubbled water. Fig. 1 Venturi effect: mixing air with water to form jetted bubbles. 11 See generally, Helfer, F., Lemckert, C., Zhang, H.. (2012): Influence of bubble plumes on evaporation from non-stratified waters. Journal of Hydrology, , Last accessed May 1,

9 agrees well with Bayar's findings. 25 ) Thus, Q w = (20 m 3 h -1 )(1000 L m -3 )(1/3600 h s -1 ) = L s -1 Thus, the typical spa pump airflow is: Q v = (0.3241)(5.556 L s -1 ) = 1.8 L s -1 Helfer measured water evaporation increases, on an absolute basis relative to baseline evaporation, by 200% 26 when bubbling 0.19 L s -1 into a tank with a surface measuring 0.90 m by 1.80 m (the air diffuser side) containing 22 C water. 27 Helfer further found that the evaporation caused by bubbling increases as the water temperature increases 28 (this reflects the increased saturation vapor density caused by higher temperatures as well as the increased convection of water molecules due to the higher temperatures). Here, though our assumed spa water temperature of 38 C is 16 C higher than the 22 C tested by Helfer, and though we know the evaporation is greater at the higher temperature, we conservatively assume the evaporation increase is the same as that measured by Helfer at the lower temperature. More significantly, Helfer calculated the evaporation due to bubble saturation when bubbling airflow at 0.19 L s -1 in water at 22 C to be 0.12 L/day. 29 Given Helfer's tank (the side with the air diffuser) measures 0.90 m by 1.80 m, 0.12 L/day water loss is: 0.12 L/day = 0.12 L/day(0.001 m 3 /L) = m 3 /day From Helfer's tank (the air diffuser side) dimensions we can calculated the water loss to be: m 3 /day / (0.90 m)(1.80 m) = m/day = mm/day Helfer found the total increase in evaporation when bubbling airflow at 0.19 L s -1 in water at 22 C to be 0.80 mm/day. 30 Thus, the ratio of evaporation due to bubble saturation to the total increase in evaporation is: ( mm/day) / (0.80 mm/day) = Therefore, less than 10% of the evaporation increase caused by bubbling is due to evaporation into the bubbles. Over 90% of the evaporation increase is due to the physical effects of bubbles 25 See generally, Baylar, A., Ozkan, F., and Unsal, M., (2010): Effect of Hole Diameter of Venturi Tube on Air Injection Rate, KSCE Journal of Civil Engineering, 14(4), pp Last accessed May 1, Id., Figure 4(b). 27 Helfer, Figure Id., Figure Id., Figure Id., Figure 4(a). 9

10 bursting at the surface. Bubbles cause small capillary waves at the surface which increase the surface area of the water, and evaporation is directly proportional to surface area. Bubbles also cause surface winds which increase evaporation; these Helfer measured to be 0.29 m s -1 at a height of 2 cm from the water surface when 0.19 L s -1 is bubbled in 22 C water. 31 Helfer's experimental apparatus had a single diffuser which bubbled vertically from the bottom of the tank. 32 The typical spa, on the other hand, has jets pushing bubbles horizontally before they emerge at the surface. This difference has two significant effects: (1) While the bubbles break the surface the same in both setups, the horizontal force of the jets, however, create a form of wind in the relative motion between the water and the air. (2) The bubbles in a horizontally jetted spa break the entire surface area of the spa (rather than just above the vertically rising bubble diffuser 33 ). As mentioned, Helfer measured a greater net evaporation due to bubbling when the water temperature was increased from 20 C to 22 C. 34 These differences cause substantially greater evaporation due to bubbling in the spa at 38 C than that measured by Helfer. As mentioned,helfer bubbled a tank with a surface area of 1.62 m 2 surface area with a single airflow diffuser which caused surface winds over only half of the tank's surface area (the winds that account for over 90% of the increase in evaporation due to bubbling). 35 But even if the typical spa's bubbles emerged vertically from the bottom (having less effect on the surface than horizontal jets do), because the assumed typical spa has 6 m 2 surface area and 4 jets, each jet would bubble a surface area of 1.5 m 2. Thus, because more of the surface area is perturbed by spa jets than Helfer's diffuser affects, the relative increase due to bubbling in a spa will again be higher on this account than that measured by Helfer. But for simplicity, and to be conservative, we extrapolate Helfer's measurements for evaporation due to bubbling at Helfer's various tested airflows by using the typical spa jet's airflow. The 1.8 L s -1 airflow calculated for the typical pump, on a per jet basis, is: Q v = (1.8 L s -1 pump -1 )(1 pump/4 jets) = 0.45 L s -1 jet -1 Figure 3 charts the extrapolated 436 % increase in evaporation (relative to baseline) at the typical spa's calculated per jet airflow is 0.45 L s -1 jet Id., Figure Id., Figure Id., Figure Id., Figure Id., Figure 7. 10

ractical Guide The following article was published in ASHRAE Journal, March 2003. Copyright 2003 American Society of Heating, Refrigerating and Air- Conditioning Engineers, Inc. It is presented for educational

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